Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
Correct Answer
$6996
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5300 × 4% × 8
= $5300 ×4/100 × 8
= 5300 × 4 × 8/100
= 21200 × 8/100
= 169600/100
= $1696
Thus, Simple Interest = $1696
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1696
= $6996
Thus, Amount to be paid = $6996 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5300
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 4% × 8)
= $5300 + ($5300 ×4/100 × 8)
= $5300 + (5300 × 4 × 8/100)
= $5300 + (21200 × 8/100)
= $5300 + (169600/100)
= $5300 + $1696 = $6996
Thus, Amount (A) to be paid = $6996 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5300, the simple interest in 1 year
= 4/100 × 5300
= 4 × 5300/100
= 21200/100 = $212
Thus, simple interest for 1 year = $212
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $212 × 8 = $1696
Thus, Simple Interest (SI) = $1696
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1696
= $6996
Thus, Amount to be paid = $6996 Answer
Similar Questions
(1) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(4) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 6% simple interest?
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?
(10) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.